Cardiac monitoring system

ABSTRACT

A method of analyzing cardiac functions in a subject using a processing system is described. The method may include applying one or more electrical signals having a plurality of frequencies to the subject and detecting a response to the applied one or more signals from the subject. A characteristic frequency can then be determined from the applied and received signals, and at least one component of the impedance (e.g., reactance, phase shift) can be measured at the characteristic frequency. Thus, the impedance or a component of impedance at a characteristic frequency can be determined for a number of sequential time instances. A new characteristic frequency may be determined within a cardiac cycle (e.g., with each sequential time instant) or the same characteristic frequency may be used throughout the cardiac cycle during which instantaneous values of impedance (or a component of impedance) are determined. These instantaneous values may be used to determine one or more indicia of cardiac function.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the continuation in part of U.S. patent applicationSer. No. 11/629,804, filed Dec. 15, 2006, now abandoned, which is aNational Stage of International Application No. PCT/AU05/000893, filedJun. 21, 2005, which application claims priority to AustralianApplication No. 2004903334, filed Jun. 21, 2004 and AustralianApplication No. 2004906181, filed Oct. 26, 2004, All of theseapplications are herein incorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

The present invention relates to methods and apparatuses for monitoringbiological parameters, and in particular to a method and apparatus formeasuring cardiac function in a subject using bioelectric impedance orcomponents of bioelectric impedance.

The reference to any prior art in this specification is not, and shouldnot be taken as, an acknowledgment or any form of suggestion that theprior art forms part of the common general knowledge.

It is estimated that coronary heart disease will become the singlebiggest public health problem in the world by 2020, The treatment ofcoronary heart disease and other cardiovascular diseases thereforerepresents and increasingly large health and economic burden throughoutthe world in the coming years.

Cardiac output (CO), which can be defined as the amount of blood ejectedby the ventricles of the heart per minute (measured in liters perminute), is governed by the metabolic demands of the body, and thereforereflect the status of the entire circulatory system. For this reasonmeasurement of cardiac output is an essential aspect of haemodynamicmonitoring of patients with heart disease or who are recovering fromvarious forms of cardiovascular disease or other medical treatments.

One existing technique for determining cardiac function which has beendeveloped is known as impedance cardiography (IC). Impedancecardiography involves measuring the electrical impedance of a subject'sbody using a series of electrodes placed on the skin surface. Changes inelectrical impedance at the body's surface are used to determine changesin tissue volume that are associated with the cardiac cycle, andaccordingly, measurements of cardiac output and other cardiac function.

A complication in impedance cardiography is that the baseline impedanceof the thorax varies considerably between individuals, the quoted rangefor an adult is 20 Ω-48 Ω at a frequency between 50 kHz-100 kHz. Thechanges in impedance due to the cardiac cycle are a relatively small(0.5%) fraction of the baseline impedance, which leads to a very fragilesignal with a low signal to noise ratio.

Accordingly, complex signal processing is required to ensuremeasurements can be interpreted.

An example of this is described in international patent publication no.WO2004/032738, In this example, the responsiveness of a patient to anapplied current is modelled using the equivalent circuit shown inFIG. 1. The equivalent circuit assumes that:

-   -   direct current is conducted through the extracellular fluid only        since the reactance of the cell membrane will be infinite;    -   an applied alternating current is conducted through the        extracellular and intracellular pathways in a ratio dependent on        the frequency of the applied signal.

Accordingly, the equivalent circuit includes an intracellular branchformed from a capacitance C representing the capacitance of the cellmembranes in the intracellular pathway and the resistance R₁representing the resistance of the intracellular fluid. The circuit alsoincludes an extracellular branch formed from resistance R_(E) whichrepresents the conductive pathway through the tissue.

WO2004/032738 operates based on the assumption that the cardiac cyclewill only have an impact on the volume of extracellular fluid in thepatient's thorax, and therefore that cardiac function can be derived byconsidering changes in the extracellular component of the impedance.This is achieved by applying an alternating current at a number ofdifferent frequencies. The impedance is measured at each of thesefrequencies and then extrapolated to determine the impedance at zeroapplied frequency, which therefore corresponds to the resistance R_(E).This is then determined to be solely due to the extracellular fluidcomponent and hence can be used to determine attributes of cardiacfunction, such as stroke volume.

However, in practice the impedance at zero frequency would not be duesolely to extracellular fluids but would be influenced by a number ofother factors. In particular, cells do not act as a perfect capacitorand accordingly, the intracellular fluid will contribute to theimpedance at a zero applied frequency.

A further issue in WO2004/032738 is that the process determines theimpedance at zero applied frequency using the “Cole model”. However,again this assumes idealised behaviour of the system, and consequentlydoes not accurately model a subject's bioimpedance response.Consequently cardiac parameters determined using these techniques tendto be of only limited accuracy.

SUMMARY OF THE INVENTION

Described herein are methods and systems for determining one or moremeasures of cardiac function. In general, these methods may involvedetermining an actual characteristic frequency, measuring theinstantaneous impedance or components of the impedance at thatcharacteristic frequency, and using the instantaneous impedance (or acomponent of the impedance) value(s) to determine a measure of cardiacfunction. A characteristic frequency may be determined by analyzing thebioelectric response of the subject's body or tissue at variousfrequencies, as described in greater detail herein. An impedance (or acomponent of the impedance such as reactance, phase shift, magnitude,resistance) may be measured either directly or derived. A characteristicfrequency may be determined for a particular subject either once, orperiodically. For example, each measurement of instantaneous impedancemay be made at a new characteristic frequency. This is described ingreater detail below.

One variation of a method of determining a measure of cardiac functionin a subject may include the steps of determining a characteristicfrequency for the subject, determining the impedance or a component ofthe impedance at the characteristic frequency, and determining a measureof cardiac function using the impedance or a component of the impedancedetermined at the characteristic frequency.

In some variations, the characteristic frequency of the subject isdetermined by applying an electrical signal having a plurality offrequencies to the subject, determining an instantaneous impedance valueat each of the plurality of frequencies, fitting the instantaneousimpedance values to a frequency dependent function, and determining thecharacteristic frequency using the function. The characteristicfrequency may be determined from an approximate maximum of the function.For example, the frequency dependent function may be a function based ona Wessel plot or a Cole plot, or a polynomial curve fit. Thecharacteristic frequency may be determined over any appropriatefrequency range. For example, the characteristic frequency may bedetermined by applying an electrical signal having a plurality offrequencies within the range of 2-10,000 kHz to the subject.

In some variations, the impedance (or a component of the impedance) atthe characteristic frequency is determined by comparing an electricalsignal applied to the subject (having a frequency at approximately thecharacteristic frequency) with an electrical signal received from thesubject in response to the applied electrical signal. The component ofimpedance determined may be the reactance, the phase (e.g., phase shift)or the magnitude. For example, the reactance or the phase shift valuesmeasured at the characteristic frequency may be used to measure (orestimate) a characteristic cardiac function. In general, multiple(“instantaneous”) values for the impedance or a component of theimpedance may be determined during the course of a cardiac cycle.

Any appropriate measure of cardiac function may be determined using thecharacteristic frequency, including stroke volume and cardiac output.For example, stroke volume may be determined by multiplying the maximumchange in impedance during a cardiac cycle by one or more constantsincluding constants based on the subject's physical characteristics. Asmentioned, the measure of cardiac function may be determined using theimpedance (or a component of the impedance) at the characteristicfrequency for a number of sequential time points. For example,instantaneous reactance values may be taken during an entire (or aportion of a) cardiac cycle. The same characteristic frequency may beused to determine the instantaneous impedance values used to determinethe measure of cardiac function, or the characteristic frequency may berepeatedly determined for each time point or a subset of time points.For example, the measure of cardiac function may be determined bydetermining the characteristic frequency and the instantaneous reactanceat the characteristic frequency for a number of sequential time points.

Also described herein are methods of determining a measure of cardiacoutput in a subject including the steps of applying an electrical signalhaving a plurality of frequencies to the subject, receiving anelectrical signal from the subject in response to the applied signal,determining a characteristic frequency for the subject by comparing theapplied and received electrical signals, determining at least onecomponent of the impedance at the characteristic frequency, anddetermining a measure of cardiac function using the at least onecomponent of the impedance determined at the characteristic frequency.As mentioned, the characteristic frequency may be determined bycomparing the applied and received electrical signals to determine aninstantaneous impedance value and fitting the instantaneous impedancevalues to a frequency dependent function. The at least one component ofthe impedance determined at the characteristic frequency may be thereactance, the phase (e.g., phase shift), the magnitude, or theresistance.

Any appropriate measure of cardiac function may be determined, includingstroke volume and/or cardiac output. For example, indicia of cardiacfunction may be determined by first identifying the characteristicfrequency, and then determining the instantaneous reactance values atthe characteristic frequency for a number of sequential time points(e.g., during a full cardiac cycle). A measure of cardiac function maybe determined by determining the instantaneous phase shift values at thecharacteristic frequency for a number of sequential time points during acardiac cycle. As mentioned above, the measure of cardiac function maybe determined by determining the characteristic frequency and at leastone component of the impedance at the characteristic frequency for anumber of sequential time points during a cardiac cycle.

Also described herein are systems for analyzing cardiac function in asubject. These systems may include a plurality of electrodes configuredto be attached to a subject, and a processor connected to the pluralityof electrodes. The processor may be configured to control theapplication of an electrical signal having a plurality of frequencies tothe subject, receive an electrical signal from the subject in responseto the applied signal, determine a characteristic frequency by comparingthe applied and received electrical signals, determine at least onecomponent of the impedance at the characteristic frequency, anddetermine a measure of cardiac function using the at least one componentof the impedance determined at the characteristic frequency. In somevariations, the system also includes a signal generator coupled toprocessor for generating the electrical signals applied to the subject.The systems may also include one or more sensors for detecting theelectrical signals from the subject in response to the appliedelectrical signals.

In some variations, the system may also include processing logic fordetermining the measure of cardiac output by multiplying the at leastone component of the impedance (e.g., reactance, phase shift) by one ormore constants including constants based on the subject's physicalcharacteristics. The processing logic may be implemented by software,hardware, or any combination of these. Thus, the processor may be amicroprocessor configured to execute the processing logic.

Any of the systems described herein may also include one or more inputdevices in communication with the processor for entering at least someof the subject's physical characteristics. For example, the systems mayinclude a keypad, mouse, memory, wireless connection or the like forreceiving input. Physical characteristics may include height, gender,weight, pulse rate, age, ethnicity, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an example of an equivalent circuit used tomodel the conduction characteristics of biological tissue.

FIG. 2 is a flowchart of an example of a process for determining cardiacfunction.

FIGS. 3A and 3B are schematics of an example of the effects of bloodflow on blood cell orientation.

FIG. 4 is a schematic of a second example of an equivalent circuit usedto model the conduction characteristics of biological tissue.

FIG. 5 is a schematic of an example of apparatus for determining cardiacfunction.

FIGS. 6A to 6C are a flowchart of a second example of a process fordetermining cardiac function.

FIG. 7 is an example of a graph of impedance plotted against frequencyfor an impedance measurement.

FIG. 8 is an example of a Wessel diagram of susceptance plotted againstconductance.

FIG. 9 is an example of three plots depicting the time varying impedanceof the thorax, the level of impedance change due to cardiac function andan ECG.

FIG. 10 is an exemplary flowchart of an example of a process fordetermining cardiac function.

FIG. 11 is another exemplary flowchart of an example of a process fordetermining cardiac function.

DETAILED DESCRIPTION OF THE INVENTION

An example of a process for determining parameters of cardiac functionrelating to a subject is described with reference to FIG. 2.

In particular at step 100, alternating electrical signals are applied tothe subject at a number of different frequencies f_(i), with electricalsignals across the subject being detected at each of the respectivef_(i), at step 110. The nature of the signals applied and detected willdepend on the implementation as will be described below.

At step 120, at a first time instance t_(n) the impedance Z_(i) at eachfrequency f_(i) is determined. At step 130, the impedance is used todetermine an intracellular impedance parameter at the time t_(n). In oneexample, this is achieved utilising an appropriate model, such as a CPE(constant phase element) model, which will be described in more detailbelow.

This is performed for a number of sequential time instance t_(n),t_(n+1), t_(n+2) until it is determined that a complete cardiac cyclehas been analyzed at step 140. This may be achieved by monitoringappropriate ECG signals, or alternatively simply by processingsufficient time instances to ensure that a cardiac cycle has beendetected.

At step 150, the intracellular impedance parameter, and in one example,changes in the intracellular impedance parameter, is used to determinecardiac parameters.

This technique takes into account that the impedance fluctuation of thethorax during the cardiac cycle is dependent on both changes in bloodvolume and changes in the impedance in the blood itself.

Blood is a suspension of erythrocytes, with a high resistivity, andother cells in a conducting fluid called plasma. The erythrocytes ofstationary blood are randomly oriented as shown in FIG. 3A, and hencethe resistivity of stationary blood is isotropic. Due to their biconcaveshape erythrocytes tend to align themselves in flowing blood with theiraxes parallel to the direction of flow as shown in FIG. 3B. Accordingly,the resistivity of flowing blood is anisotropic.

The anisotropy of the resistivity is due to the longer effective pathlength for the current travelling normal to the axis of the vesselcompared with the current flowing parallel to the vessel. As a result,the resistance of the intracellular fluid alters depending on theorientation of the erythrocytes, and hence depends on the flow of blood.

Furthermore, the extent of the anisotropy is shear-rate dependent sincethe orientation of the erythrocytes is influenced by the viscous forcesin flowing blood. As a result, the resistivity is in turn also dependenton the flow rate.

It is therefore possible to take this into account by determiningcardiac function on the basis of intracellular parameters, as opposed tousing extracellular impedance parameters as in the prior art. This cantherefore be achieved using the equivalent circuit shown in FIG. 1, andby using the impedance measurements to determine the impedanceparameters based on the capacitance C and the resistance R₁ of theintracellular branch.

Thus, in this instance, the impedance measurements can be used todetermine values for the intracellular resistance R_(T) and thecapacitance C, for example, by determining values of R₀ and R_(ω), andthen using these to solve the Cole equation using appropriatemathematical techniques.

In this instance however, modelling the resistivity as a constant valuedoes not accurately reflect the impedance response of a subject, and inparticular does not accurately model the change in orientation of theerythrocytes, or other relaxation effects.

To more successfully model the electrical conductivity of blood, animproved CPE based model can be used as will now be described withrespect to FIG. 4.

In this example, to accurately determine the characteristic impedance,and interpret the contribution of cardiac effects to the impedance, anequivalent circuit based on a free conductance parallel model is used,as shown in FIG. 4. Such a model can also be created in a series formand the parallel model is shown here for illustration.

In this example, the circuit includes an extracellular conductance G₀that represents the conductance of electrical current through theextracellular fluid. The intracellular conduction path includes aconstant phase element (CPE) represented as the series connection of afrequency dependent conductance, and a frequency dependent capacitance.

The two equations below define a general CPE:Y _(CPE)=(ωτ)^(m)(G _(mτ=1) +jB _(ωτ=1))  (1)

$\begin{matrix}{\varphi_{cpe} = \frac{\arctan\mspace{11mu} B}{G}} & (2)\end{matrix}$where:

-   -   Y_(CPE) is the admittance of the CPE and    -   φ_(cpe) is the phase of the CPE.

In this equation τ represents a frequency scale factor and, ωτ isdimensionless.

The parameter m defines the extent of the frequency dependence of theadmittance of the CPE Y_(CPE) and the frequency scale factor with τ. Itis known that for biological tissue m is in the range of 0≦m≦1.

In one example, the CPE is in accordance with Fricke's law (CPE_(F))although other forms of CPE could be used. It is usual practice to usethe exponent symbol α (m=α) for Fricke CPE's.

In order to make the model compatible with relaxation theory, the seriesideal resistor is changed to a free resistor parameter R_(var) so thatthe characteristic time constant τ_(r) will be a dependent parameter.

The result is that the conductance of the circuit can be expressed asfollows:

$\begin{matrix}{Y = {G_{0} + \frac{1}{R_{var} + {R_{1}( {j\omega\tau}_{z} )}^{- \alpha}}}} & (3) \\{\tau_{Ym} = {\frac{1}{\omega_{Ym}} = {\tau_{Y}( \frac{R_{1}}{R_{var}} )}^{\frac{1}{- \alpha}}}} & (4)\end{matrix}$

Here τ_(Ym) is a new characteristic time constant. The subscript m isused to identify the new variable from the previous variables and isconsistent with the nomenclature know to those skilled in the art.

By putting a nominal fixed value to the time constant τ_(y) it ispossible to follow the CPE by calculating the R₁ using the equation.

$\begin{matrix}{R_{1} = \frac{R_{var}}{( {\tau_{Y}\omega_{Ym}} )^{- a}}} & (5)\end{matrix}$

In this instance, the variable resistance parameter R_(var) is dependenton the orientation of the erythrocytes and as a result, changes inR_(var) can be used to determine the rate of flow of blood within asubject. Consequently, it is possible to determine information regardingcardiac output, or the like.

An example of apparatus suitable for performing an analysis of asubject's bioelectric impedance to determine cardiac function will nowbe described with reference to FIG. 5.

As shown the apparatus includes a processing system 10 having aprocessor 20, a memory 21, an input/output (I/O) device 22 and aninterface 23 coupled together via a bus 24. The processing system iscoupled to a signal generator 11 and a sensor 12 as shown. In use thesignal generator 11 and the sensor 12 are coupled to respectiveelectrodes 13, 14, 15, 16, as shown.

In use, the processing system 10 is adapted to generate control signals,which causes the signal generator 11 to generate an alternating signalwhich is applied to a subject 17, via the electrodes 13, 14. The sensor12 then determines the voltage or current across the subject 17 andtransfers appropriate signals to the processing system 10.

Accordingly, it will be appreciated that the processing system 10 may beany form of processing system which is suitable for generatingappropriate control signals and interpreting voltage data to therebydetermine the subject's bioelectrical impedance, and optionallydetermine the cardiac parameters.

The processing system 10 may therefore be a suitably programmed computersystem, such as a laptop, desktop, PDA, smart phone or the like.Alternatively the processing system 10 may be formed from a specialisedhardware. Similarly, the I/O device may be of any suitable form such asa touch screen, a keypad and display, or the like.

It will be appreciated that the processing system 10, the signalgenerator 11 and the sensor 12 may be integrated into a common housingand therefore form an integrated device. Alternatively, the processingsystem 10 may be connected to the signal generator 11 and the sensor 12via wired or wireless connections. This allows the processing system 10to be provided remotely to the signal generator 11 and the sensor 12.Thus, the signal generator 11 and the sensor 12 may be provided in aunit near, or worn by the subject 17, whilst the processing system issituated remotely to the subject 17.

In practice, the outer pair of electrodes 13, 14 are placed on thethoracic and neck region of the subject and an alternating signal isapplied at a plurality of frequencies either simultaneously or insequence, (two are sufficient but at least three are preferred with fiveor more being particularly advantageous) in the range 2-10,000 kHz.However the applied waveform may contain more frequency componentsoutside of this range.

In the preferred implementation the applied signal is a frequency richvoltage from a voltage source clamped so it does not exceed the maximumallowable patient auxiliary current. The signal can either be constantcurrent, impulse function or a constant voltage signal where the currentis measured so it does not exceed the maximum allowable patientauxiliary current.

A potential difference and/or current are measured between an inner pairof electrodes 16, 17. The acquired signal and the measured signal willbe the superposition of signals at each of the applied frequencies andthe potentials generated by the human body, such as the ECG.

Optionally the distance between the inner pair of electrodes may bemeasured and recorded. Similarly, other parameters relating to thesubject may be recorded, such as the height, weight, age, sex, healthstatus, and other information, such as current medication, may also berecorded.

The acquired signal is demodulated to obtain the impedance of the systemat the applied frequencies. One suitable method for demodulation is touse a Fast Fourier Transform (FFT) algorithm to transform the timedomain data to the frequency domain. Another technique not requiringwindowing of the measured signal is a sliding window FFT. Other suitabledigital and analog demodulation techniques will be known to personsskilled in the field.

Impedance or admittance measurements are determined from the signals ateach frequency by comparing the recorded voltage and current signal. Thedemodulation algorithm will produce an amplitude and phase signal ateach frequency.

An example of the process of measuring a subject's bioelectric impedanceand then interpreting this will be described in more detail withreference to FIGS. 6A to 6C.

At step 200 the processing system 10 generates predetermined controlsignals causing the signal generator 11 to apply current signals to thesubject 17 at a number of frequencies f_(i), over a time period T. Thecurrent signals applied to the subject 17 may be provided at thefrequencies f_(i) sequentially, or simultaneously, by superposing anumber of signals at each corresponding frequency f_(i).

It will be appreciated that the control signals are typically generatedin accordance with data stored in the memory 21 and this can allow anumber of different current sequences to be used, with selection beingmade via the I/O device 22, or via another appropriate mechanism.

At step 210 the sensor 12 measures the voltage across the subject 17. Inthis regard, the voltage signals will typically be analogue signals andthe sensor 12 will operate to digitise these, using an analogue todigital converter (not shown).

At step 220 the processing system 10 samples the signals from the signalgenerator 11 and the sensor 12, to thereby determine the current andvoltage across the subject 17.

At step 230, a filter is optionally applied to the voltage signals atstep 230 to remove respiratory effects, which typically have a very lowfrequency component in line with the patient's rate of breathing. Itwill be appreciated that filtering may be achieved by the sensor 12 orthe processing system 10, depending on the implementation.

At step 240 ECG vectors are optionally extracted from the voltagesignals. This can be achieved as the ECG signals typically have afrequency in the region 0 Hz to 100 Hz, whereas the impedance signalsare in the region of 5 kHz to 1 MHz. Accordingly, the ECG signals may beextracted by any suitable technique, such as demodulation, filtering orthe like.

At step 250 the signals may also undergo additional processing. This canbe performed, for example, by further filtering the signals to ensurethat only signals at the applied frequencies f_(i), are used inimpedance determination. This helps reduce the effects of noise, as wellas reducing the amount of processing required.

At step 260, the current and voltage signals sampled at time t_(n) todetermine the impedance Z_(i) at each frequency f_(i).

At step 270 a function is fitted to the impedance values.

An example of this is shown in FIG. 7, which shows an example of theappearance of the impedance data and function when plotted againstfrequency. It will be appreciated that the plot is for the purpose ofexample only, and in practice the processing system 10 will notnecessarily generate a plot. In the case of the frequency versus theimpedance plot shown in FIG. 7, the function is typically a polynomialand in particular in this example is a sixth order polynomial.

Alternatively a Wessel plot may be used as shown in FIG. 8, as will bedescribed in more detail below.

In practice noise elimination may be necessary to accurately fit afunction to the data. In one example, elimination of noise at certainfrequencies can be performed by initially fitting a function to themeasured data and then systematically removing outlier points from thedata set and re-fitting the function to the reduced data set.

Accordingly, at step 280 the processing system 10 operates to determineif there are outlier points, which are considered to be points that aregreater than a predetermined distance from the determined function.

It will be appreciated that the function used, and the determination ofoutlier points may be achieved utilising standard mathematicaltechniques.

If it is determined that there are outlier points, these are removedfrom the data set and a new function fitted to the remaining values atstep 290. At step 290 the processing system 10 determines if the fit isimproved and if so the outlier point is excluded from the data setpermanently with the new function being assessed at step 310. This isrepeated until all outliers that affect the data are removed.

If it is determined that the fit is not improved at step 300 the outlieris retained and the previous function used at step 320.

If there are no outliers, or once outliers have been excluded from thedata set, the plot is then used to determine values from R_(o) and R_(∝)using the determined function.

In one example, the function is used to calculate R₀ and R_(∝).Alternatively, this can be used to determine the impedance at thecharacteristic frequency. As is apparent to one of skill in the art, thecharacteristic frequency is apparent from this procedure (e.g., themaximum reactance in the frequency range).

For example, in the case of the function shown in FIG. 7, R_(∝) can bedetermined by finding the impedance at the start of the pseudo-plateau,i.e. a relatively flat portion, on the curve of FIG. 7. In theillustrative embodiment the pseudo plateau is identified using arule-based approach.

In this approach the function is analysed to find the frequency whereimpedance (Z) changes (ΔZ) by less than 1% with a frequency increase of25 kHz. The resistance or impedance Z measured at this frequency isidentified as R_(∝) and represents resistance of the circuit if aninfinitely high frequency was applied. Other methods of determining thispseudo-plateau region may be known to those skilled in the art.

Similarly, the impedance at zero applied frequency R₀ can be determinedas the value at which the function would intercept the y-axis.

If a “Wessel” plot type function is used, as shown in FIG. 8, thisapproach uses an arc, which allows the characteristic impedance to bedetermined. In this example, the apex of the arc in the complex Wesselplane no longer corresponds to the nominal value of τ_(Y), but to τ_(Ym)as given by the above equation. In some variations, the characteristicfrequency (the frequency at the character impedance) may be determinedby solving a Cole-Cole model for the peak. Thus, the characteristicfrequency may be determined directly (e.g., by extrapolating from acurve fitting), or it may be numerically determined. J. Xiang et al.,(“On the Adequacy of Identified Cole-Cole Models,” Computers &Geosciences 29 (2003); 647-654) describes methods of numericallydetermining a Cole-Cole model that may be used to determine thecharacteristic frequency.

Additionally α can be determined from the angle subtended by the arcuatelocus from R₀ to R_(∝). By comparing this to m determined fromsusceptance data, this allows whether the Fricke criteria for relaxationphenomena of biological materials is met. In the event that they areequal or within a predetermined range of each other, then the Wesseldiagram method may be applied with reasonable accuracy. In the eventthat m and α are not sufficiently close in value then the functionfitting approach described above is a more appropriate method fordetermining the quantities of interest for the free conductance model.

At step 340 the processing system 10 uses the values of either R₀ toR_(∝), or the characteristic impedance, together with equation (5) todetermine the intracellular impedance parameter, which in this exampleis the intracellular variable resistance parameter R_(var).

As an alternative to determining values of R₀, R_(∝), or thecharacteristic impedance Z_(o), the equation (5) can alternatively besolved mathematically, for example by using a number of differentimpedance values at different frequencies f_(i) to solve a number ofsimultaneous equations. These values can be based on directly measuredvalues, although preferably these are values determined from the fittedfunction, to thereby take into account the impedance response across therange of applied frequencies f_(i).

At step 350 it is determined if a full cardiac cycle has been completedand if not the process returns to step 240 to analyse the next timeinstance t_(n+1).

At step 360, once a full cardiac cycle has been completed, theprocessing system 10 operates to determine the change in theintracellular resistance parameter R_(var) over the cardiac cycle beforeusing this to determine cardiac parameters at step 370.

A typical plot of the time varying impedance obtained by the presentmethod is shown in FIG. 9.

In FIG. 9 the raw impedance data is plotted against time (measured bysample number) in the top graph. This graph includes the impedance fromall time varying impedance components in the thoracic cavity includingvariation in blood volume, blood cell orientation and changes due torespiration.

The centre graph of FIG. 9 depicts the rate of change of impedanceattributable to cardiac function of a patient. The graph was generatedby removing the low frequency components from the top graph andobtaining the rate of change of impedance from the remaining data.

As will be appreciated by those skilled in the art additionalmeasurements can also be incorporated into the present method orconducted simultaneously. For example, the inner electrodes can also beused to record ECG vectors. In order to generate more ECG vectors moreinner electrode combinations are required. The outer electrodes can alsobe used to record the ECG vectors. The processing unit, or the operator,can automatically or manually select the most appropriate ECG vector. Anexternal ECG monitor can also be connected or alternatively a separatemodule can be incorporated into the invention with additional electrodesto calculate the ECG vectors.

The ECG can advantageously be used to aid in the determination ofcardiac events. An example ECG output is depicted in the lower graph ofFIG. 9.

To calculate certain cardiac parameters from the impedance waveform,fiducial points must also be suitably identified. The ECG data and/orother suitable physiological measurement techniques may be employed toaid this process.

Other physiological parameters that could be used to assist inidentifying fiducial points in the cardiac cycle includeinvasive/non-invasive blood pressure, pulse oximetry, peripheralbioimpedance measurements, ultrasound techniques and infrared/radiofrequency spectroscopy. Such techniques can be used singularly or in aplurality to optimally determine cardiac event timing.

In one example an artificial neural network or weighted averages todetermine the cardiac events as identified by conductance measurementscombined with other methods of physiological measures offer an improvedmethod of identifying these points. In the present example the start andend of left ventricular ejection are indicated by the vertical lines onthe graphs of FIG. 9. The time between these points is the leftventricle ejection time (LVET).

These fiducial points can be used to obtain impedance values ofinterest. For example, the maximum rate of change in the intracellularresistance value R_(var) over left ventricle ejection which is indicatedon the central graph of FIG. 9 as:

$( \frac{\mathbb{d}{R_{var}(t)}}{\mathbb{d}t} )_{MAX}$

Measures of cardiac function can then be determined from this data. Forexample, the following method can be used to calculate blood velocityand stroke volume. The present example uses impedance measures tocalculate cardiac output. However the same functions can be describedusing admittance or a combination of the two. The following formula canbe used to calculate cardiac output:

${CO} = {k_{1}{c_{1}( \frac{( \frac{\mathbb{d}{R_{var}(t)}}{\mathbb{d}t} )_{MAX}}{Z_{0}} )}^{n}*( \frac{1}{T_{RR}} )^{m} \times T_{LVE}}$

Where:

-   -   CO denotes cardiac output (liters/min),

$( \frac{\mathbb{d}{R_{var}(t)}}{\mathbb{d}t} )_{\max}$

-   -    is as indicated on FIG. 9;    -   k₁ is an optional population specific correction factor based on        one or more subject parameters, such as at least the height and        weight, but can also include distance between the electrodes and        age;    -   c₁ is an optional calibration coefficient used to convert the        units from Ohmic units to liters (which may be uniquely defined        at manufacture for each monitoring device used to implement the        method),    -   Z₀ is an optional baseline Impedance measured at the        characteristic frequency (between 10 Ohms and 150 Ohms),    -   T_(RR) is the interval between two R waves obtained from the ECG        (found from the ECG or impedance or conductance data),    -   T_(LVE) is left ventricular ejection time (measured from either        the conductance or impedance curve or preferably a combination        of other physiological measurement techniques) and    -   n (range . . . 4>n<4) and m (range . . . 4>m<4) are optional        constants.

The person skilled in the art will be able to determine appropriatevalues for these constants dependent upon the patient and situation inwhich the method is applied.

Whilst the example described above has been described in the context ofproviding determining cardiac output of the heart, embodiments of thepresent invention can be applied to determine other measures of cardiacperformance, including but not limited to, stroke volume, cardiac index,stroke index, systemic vascular resistance/index, acceleration,acceleration index, velocity, velocity index, thoracic fluid content,left ventricular ejection time, Pre-ejection period, systolic timeratio, left cardiac work/index, heart rate and mean arterial pressure.

As described briefly above, measures of cardiac performance and functionmay also be determined using the characteristic frequency. Thus, thecharacteristic frequency may be determined during a cardiac cycle byapplying an electrical signal having a plurality of frequencies (ormultiple electrical signals at different frequencies), detectingelectrical signals in response to the applied signals, processing thedetected signals (e.g., to remove unwanted components such as ECGs andother signals), comparing the applied electrical signals at eachfrequency with the response signals at each frequency, and fitting thesignals to a function from which the characteristic frequency may bedetermined. As previously described, FIGS. 6A and 6B illustrate this. Inthis example, instantaneous impedance values are determined for eachfrequency f_(i) at time t_(o) 260, and are fit to a function 270 (suchas the Wessel plot shown in FIG. 8). The characteristic frequency may beidentified from the function. For example, the characteristic frequencyfrom the Wessel plot is the frequency at the top of the arch (e.g., thefrequency with the largest reactance). In practice, the characteristicfrequency may be determined by approximating the maximum reactance overthe applied frequency range.

The signal(s) applied to the subject may be a signal (or signals) havinga plurality of frequency components, or a series of signals at differentfrequencies. The response signal that is measured from the subject afterthe application of one or more electrical signals arises because of theelectrical properties of the body. This response is usually referred toas a response signal. The response signal may also be referred to as anevoked response or evoked signal, and is typically a passive response.For example, the response does not usually include a regenerative evoked(e.g., active) response from electrically active tissue.

Once the characteristic frequency has been determined, thischaracteristic frequency may provide a relatively accurate means ofdetermining cardiac function by then applying an electrical signal atthe characteristic frequency and receiving the response electricalsignal at that frequency. This electrical stimulation and sampling maybe repeated during a complete or partial cardiac cycle. For each timepoint, the stimulated and response signals may be compared (e.g., afterfiltering or other signal processing) to determine an instantaneousimpedance or any components of the instantaneous impedance, such asresistance, reactance, phase and magnitude. As is known in the art, theresistance and reactance, and the impedance and phase are allmathematically related, and with any two you can calculate the othertwo. Further, as is known in the art, any of these components can bedetermined from the applied and response signals.

For example, in FIG. 6C, R_(var) is determined iteratively bycalculating instantaneous impedance values at a plurality of frequenciesat each time point. FIGS. 10 and 11 describe an alternative method ofdetermining a measure of cardiac function, by instead determining thecharacteristic frequency (stimulating at multiple frequencies) and usingthis characteristic frequency to determine the instantaneous impedance(or components of the instantaneous impedance). The step of determininga characteristic frequency may be performed only once during a cardiaccycle, or only periodically during a cardiac cycle, rather than at eachtime point t_(i).

FIG. 10 is a schematic flowchart further illustrating one method ofdetermining a measure of cardiac function in a subject. First, acharacteristic frequency for the subject 1001 is determined. Aspreviously described, the characteristic frequency may be determined byapplying an electrical signal (or signals) having a plurality offrequencies to the subject, receiving the response signal(s) from thesubject, and determining an instantaneous impedance value (or acomponent of the impedance) at each of the plurality of frequencies,fitting the values to a function (e.g., a frequency dependent function),and determining the characteristic frequency using the function. Anyappropriate range of frequencies may be used, including frequenciesbetween 2 and 10,000 kHz (e.g., 2-200 kHz, etc.), and any appropriatenumber of frequencies may be used (e.g., 2, 8, 16, 50, 100, etc.).Although the instantaneous impedance values may be determined at eachtime point, in some variations components of the instantaneous impedancevalues (e.g., reactance and/or resistance) are determined at each timepoint, rather than the combined impedance value. In some variations,phase is used.

Next, the impedance, or a component of the impedance, can be determinedat different time points during all or part of a cardiac cycle 1003. Asdescribed above, the intracellular resistance may be calculated from theimpedance. In some variations the reactance component of the impedanceis determined at different time points of a cardiac cycle by applyingelectrical signals at the characteristic frequency. Thus, at least onereactance time point may be determined at that characteristic frequency.This reactance time point may be referred to as an instantaneousreactance at that time point. In some variations the component of theimpedance determined at each time point using the characteristicfrequency is phase, magnitude (or both). In some variations theinstantaneous impedance is determined using the characteristic frequencyat each time point.

In FIG. 10, the impedance (or a component of the impedance) at thecharacteristic frequency is determined at discrete time points during acomplete cardiac cycle 1005. Any number of time points within thecardiac cycle may be taken (e.g., the number of sample points within thecardiac cycle). Although most of the methods described herein takemeasurements over a full cardiac cycle, a portion of a cardiac cycle ormultiple cardiac cycles may also be used. As briefly mentioned above,these instantaneous values determined during the cardiac cycle using thecharacteristic frequency may be stored for use in determining a cardiacfunction such as stroke volume or cardiac output.

As mentioned above, a new characteristic frequency may be determinedduring the cardiac cycle, as indicated by the dashed line 1011 in FIG.10. For example, a new characteristic frequency may be determined foreach time point, or for some subset of time points.

Finally, a measure of cardiac function may be determined using theinstantaneous impedance (or a component of impedance) value(s)determined at the characteristic frequency 1007 in the previous steps.For example, the instantaneous impedance values measured at thecharacteristic frequency may be used to determine a stroke volume and/orcardiac output. The maximum change in impedance, (dz/dt)_(max), isproportional to the stroke volume and also to the cardiac output. Forexample, stroke volume may be represented as:

${SV} = \frac{L^{\prime\; 3}\langle \frac{\mathbb{d}z}{\mathbb{d}t} \rangle_{\max}{VET}}{Z_{B}}$where: SV=stroke volume, (dz/dt)_(max)=maximum rate of change inmeasured impedance at the beginning of systolic cycle, VET=leftventricular ejection time, and L′=thoracic length estimated from thesubject's height and weight using a nomogram. L′ also accounts for bloodresistivity. Z_(B) is a baseline impedance value. Thus, the constantsmay be combined, expressing the stroke volume in terms of elements(e.g., (dz/dt)_(max)) that may be determined for each cardiac cycle.Cardiac output is related to stroke volume (e.g., cardiacoutput=SV*heart rate).

In one example, the instantaneous reactance at the characteristicfrequency may be used to determine a measure of cardiac function. Forexample, the instantaneous reactance at the characteristic frequency canbe measured at each sample point during a cardiac cycle by stimulatingthe subject at the characteristic frequency. The change in the reactance(dX/dt)_(max) is also proportional to the stroke volume and the cardiacoutput, and may therefore be used (in conjunction with appropriatemonograms) to determine these measures of cardiac function. FIG. 11illustrates this exemplary method.

A system for analyzing cardiac function in a subject may include any ofthe elements described above, and may also include one or moreprocessors for executing the procedures described herein. For example, asystem may include a processor (e.g., microprocessor) for controllingthe application of an electrical signal having a plurality offrequencies to the subject 1101. Thus, the processor may be connected toa signal generator and electrodes to be connected to the subject forstimulation. The controller may also be connected to electrodes forreceiving an electrical signal from the subject in response to theapplied signal 1103. The input signal may also be sent to thecontroller, and both the input and output signals may be digitized,filtered, or otherwise conditioned. The processor may further determinea characteristic frequency by comparing the applied and receivedelectrical signals 1105, as described above.

The characteristic frequency may then be used to determine aninstantaneous reactance, or any other appropriate characteristic ofimpedance, including phase 1107. For example, the system may detect therelative phase shift (dφ/dt) between the injected signal and theresponse signal at discrete times during a full cardiac cycle or aportion of a cardiac cycle by applying an electrical signal at thedetermined characteristic frequency and comparing the phase of theresponse signal to the applied signal. As mentioned above, in somevariations, the characteristic frequency may be determined once duringthe cardiac cycle (e.g., at the start of the measurement), or a newcharacteristic frequency may be determined before determining thecomponent of the impedance (e.g., reactance or phase shift) at each timepoint, as indicated by the dashed line 1117 in FIG. 11. In somevariations, a new characteristic frequency may be recalculated aftersome number of data point (or a fraction of the cardiac cycle).

These instantaneous impedance values determined at the characteristicfrequency (e.g., the instantaneous impedance, instantaneous reactance,instantaneous phase shift, etc.) may be stored by the system. Forexample, the processor may include a memory to store these values. Insome variations all of the values are not stored, but only a runningvalue (e.g., the maximum value, a sum of the values, a product of thevalues, etc.) is stored. These stored values may be used to determine ameasure of cardiac function 1111. For example, the phase shift (dφ/dt)values may be used to determine stroke volume and/or cardiac output. Forexample, the phase shift may be proportional to the changes in bloodflow in the aorta, as previously described. Thus, the stroke volume maybe expressed as:SV=C′*(dφ/dt)_(max)*VETwhere VET is ventricular ejection time, and C′ is a constant that may bebased on individual patient characteristics (including height, weight,gender, age, etc.). As previously described, the VET may be determinedfor each cardiac cycle. For example, the ECG may be used to determinethe length of each heart beat, as well as the start of ejection and theend of ejection, from which VET can be estimated. Heart rate (andtherefore cardiac output) may also be determined from the phaseinformation.

The measure of cardiac function determined may be displayed, stored ortransmitted. Thus, any of the systems for analyzing cardiac functiondescribed herein may include a display (e.g., screen, printer, etc.) ortelemetry (wireless, LAN, etc.), or the like. The systems describedherein may also include one or more inputs such as keyboards, mouse,touch screen, etc. for inputting subject information.

Persons skilled in the art will appreciate that numerous variations andmodifications will become apparent. All such variations andmodifications which become apparent to persons skilled in the art,should be considered to fall within the spirit and scope that theinvention broadly appearing before described.

1. A method of determining a measure of cardiac function in a subject,the method comprising: (a) determining a characteristic frequency forthe subject, wherein the characteristic frequency is the most negativereactance within an applied frequency range; (b) determining theimpedance phase angle at the characteristic frequency; and (c)determining a measure of cardiac function using the impedance phaseangle determined solely at the characteristic frequency and displaying,storing, or transmitting the measure of cardiac function.
 2. The methodof claim 1, wherein the characteristic frequency of the subject isdetermined by: (a) applying an electrical signal having a plurality offrequencies to the subject; (b) determining an instantaneous impedancevalue at each of the plurality of frequencies; (c) fitting theinstantaneous impedance values to a frequency dependent function; and(d) determining the characteristic frequency using the function.
 3. Themethod of claim 2, wherein the characteristic frequency is determinedfrom an approximate maximum of the function.
 4. The method of claim 2,wherein the frequency dependent function is a function based on a Wesselplot or a Cole plot.
 5. The method of claim 2, wherein the frequencydependent function is a polynomial curve fit.
 6. The method of claim 1,wherein the characteristic frequency is determined by applying one ormore electrical signal having frequencies within the range of 2-10,000kHz to the subject.
 7. The method of claim 1, wherein the impedancephase angle at the characteristic frequency is determined by comparingan electrical signal applied to the subject having a frequency atapproximately the characteristic frequency to an electrical signalreceived from the subject in response to the applied electrical signal.8. The method of claim 1, wherein the step of determining the impedancephase angle at the characteristic frequency comprises determining aninstantaneous reactance.
 9. The method of claim 1, wherein the step ofdetermining the impedance phase angle at the characteristic frequencycomprises determining an instantaneous phase shift.
 10. The method ofclaim 1, wherein a stroke volume is determined as the measure of cardiacfunction.
 11. The method of claim 10, wherein the stroke volume isdetermined by multiplying the maximum change in reactance during acardiac cycle by one or more constants including constants based on thesubject's physical characteristics.
 12. The method of claim 1, wherein acardiac output is determined as the measure of cardiac function.
 13. Themethod of claim 1, wherein the measure of cardiac function is determinedby determining the phase angle at the characteristic frequency for anumber of sequential time points during a cardiac cycle.
 14. The methodof claim 1, wherein the measure of cardiac function is determined bydetermining the reactance at the characteristic frequency for a numberof sequential time points during a cardiac cycle.
 15. The method ofclaim 1, wherein the measure of cardiac function is determined bydetermining the characteristic frequency and the phase angle at thecharacteristic frequency for a number of sequential time points during acardiac cycle.
 16. A method of determining a measure of cardiac functionin a subject, the method comprising: (a) applying an electrical signalhaving a plurality of frequencies to the subject; (b) receiving anelectrical signal from the subject in response to the applied signal;(d) determining a characteristic frequency for the subject by comparingthe applied and received electrical signals, wherein the characteristicfrequency is the most negative reactance within an applied frequencyrange; (c) determining the impedance phase angle at substantially thecharacteristic frequency; and (d) determining a measure of cardiacfunction using the impedance phase angle determined solely at thecharacteristic frequency and displaying, storing, or transmitting themeasure of cardiac function.
 17. The method of claim 16, further whereinthe characteristic frequency is determined by comparing the applied andreceived electrical signals to determine an instantaneous impedancevalue and fitting the instantaneous impedance values to a frequencydependent function.
 18. The method of claim 16, wherein the measure ofcardiac function is selected from the group consisting of: stroke volumeand cardiac output.
 19. The method of claim 16, wherein the measure ofcardiac function is determined by determining the phase shift at thecharacteristic frequency for a number of sequential time points during acardiac cycle.
 20. A system for analyzing cardiac function in a subject,the device comprising: a plurality of electrodes configured to beattached to a subject; and a processor connected to the plurality ofelectrodes, the processor configured to execute processing logic, theprocessing logic configured to: (a) control the application of anelectrical signal having a plurality of frequencies to the subject; (b)receive an electrical signal from the subject in response to the appliedsignal; (c) determine a characteristic frequency by comparing theapplied and received electrical signals, wherein the characteristicfrequency is the most negative reactance within an applied frequencyrange; (d) determine the impedance phase angle at the characteristicfrequency; and (e) determine a measure of cardiac function using theimpedance phase angle determined solely at the characteristic frequency.21. The system of claim 20, further comprising a signal generatorcoupled to processor for generating the electrical signals applied tothe subject.
 22. The system of claim 20, further comprising one or moresensors for detecting the electrical signals from the subject inresponse to the applied electrical signals.
 23. The system of claim 20,further comprising processing logic for determining the measure ofcardiac function by multiplying the impedance phase angle by one or moreconstants including constants based on the subject's physicalcharacteristics.
 24. The system of claim 20, further comprising an inputdevice in communication with the processor for entering at least some ofthe subject's physical characteristics.